Soldify modifier leaves gap instead of thickness?
Since your mesh is just vertices and edges, the solidify modifier faithfully maintains the lack of faces. Therefore you will likely want to use 'Grid Fill' to fill in the shape with quads, or manually do so by selecting three connected edges on your loop and pressing 'f' to fill them in with a face (automatically creating the edge necessary to form a closed shape) and then repeating that process with using the new edge. Note that grid fill requires there to be an even number of verts, so try adding a new one if it causes an issue.